Electrical – Simulink Modeling Problem

Your approach should work. It's also the simplest way to solve the problem.

You could always work out a position controller that steers directly the motors, but it would be less easy to understand how to tune it. And I understand you have both position and velocity readings, so why not using two loops?

As people's comments to your question highlight, obviously you'd now have a position controller rather than velocity. But it makes sense as it's for a robot.

You need to be careful to a few details:

1. If the two DC motors are working in parallel, you must find a way for the two not to interfere with each other (like forcing load sharing). However you must have faced this problem already in the speed loop.
2. The external loop (position control) is bound to be far slower than the speed loop. If it worked at the same pace, or faster, you'd have the position loop strongly pulling on the speed one without letting it the time to react, and you'd have strong interactions or even instabilities. I suggest that you speed up the internal one (speed) as much as you can, and then tune the external one.
3. The external loop shall here be your 'precise' one. The internal one should just be quick in reaction rather than precise. I'd suggest a P or PD controller for the internal one, and PI or PID for the external one.

Extra tip: as it's for a robot, I'd take into consideration a position reference feed-forward.

Do you connect the PID such that the controller sets the current to a certain level, or do you connect the PID such that the controller adds/subtracts current to the instantaneous current to reach the desired level?

There are different PID algorithms that do either of those two things. The latter type is called a velocity algorithm (because it controls the velocity of a hypothetical mechanical valve motion rather than the position of the valve). Since the valve performs the integration there were once some advantages to this method- for one thing it automatically stops integrating when the actuator hits the limit, which helps with overshoot due to integrator windup. However, if you are using derivative control it must be double differentiated- which tends to make that contribution very noisy.

By the way, controlling the current through the resistor is usually not a good idea. What you want to do (typically) is to control the power. The resulting nonlinearity from voltage control will usually make the controller hard to tune well over a range of setpoints (it will either be too sluggish or not stable enough).